If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes. What type of problem is this? Poisson Random variable Sample mean Sample proportion Normal

a) The probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes = 0.309

b) Check the beginning of Explanation for which type of dustribution this is.

Step-by-step explanation:

A distribution with the mean given and the spread around the mean (standard deviation) given, is a normal distribution. Especially as it shows that the distribution is symmetric around the mean.

To find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes.

We first standardize '3 minutes'.

The standardized score is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (3 - 3.5)/1 = - 0.5

probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes.

P(x < 3) = P(z < -0.5)

We'll use data from the normal probability table for these probabilities

P(x < 3) = P(z < -0.5) = 1 - P(z ≥ - 0.5) = 1 - P(z ≤ 0.5) = 1 - 0.691 = 0.309.